The angular distribution of integral ideal numbers with a fixed norm in quadratic extensions

TL;DR

This paper generalizes the study of angular distribution of Gaussian integers with fixed norm to integral ideal numbers in any quadratic extension, expanding understanding of their geometric distribution.

Contribution

It extends Erdős and Hall's results from Gaussian integers to integral ideal numbers in all quadratic extensions, broadening the scope of angular distribution analysis.

Findings

Established the angular distribution pattern in quadratic extensions.

Generalized previous results from Gaussian integers to all quadratic fields.

Provided new insights into the geometric properties of ideal numbers.

Abstract

Erd\H{o}s and Hall studied the angular distribution of Gaussian integers with a fixed norm. We generalize their result to the angular distribution of integral ideal numbers with a fixed norm in any quadratic extension.